Solve the problem. A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved. A brine containing 2lb/gal of sait runs into the tank at the rate of 4 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 3 gal/min. Find the solution to the differential equation that models the mixing process.

Solve the problem. A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved. A brine containing 2lb/gal of sait runs into the tank at the rate of 4 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 3 gal/min. Find the solution to the differential equation that models the mixing process.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Solve the problem.
A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved. A brine containing 2 lb/gal of sait runs into the tank at the rate of 4
gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 3 gal/min. Find the solution to the differential equation
that models the mixing process.

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